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31 January, 08:02

The relationship between the time a politician has been in office and his approval rating can be modeled by the equation y = - 0.01x + 70, where x is his time in office in days and y is his approval rating as a percent. Which of these statements is true according to the model?

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  1. 31 January, 08:27
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    Because of absence of options, I have listed statements that are true; according to the model.

    Step-by-step explanation:

    To answer this, we find all possible explanations to the model. First, we know that:

    X = time in office (in days)

    Y = approval rating (in percentage)

    The constant term in the model is 70

    So the true statements that can be derived are:

    (A) Y is inversely related to X. This is obvious because of the difference in sign of the coefficient of Y and that of X.

    The coefficient of Y is + 1

    The coefficient of X is - 0.01

    Y has a positive coefficient while X has a negative coefficient.

    The inverse relationship hence implies that the more days the politician spends in office, the less his percentage approval rating (and vice versa) !

    Testing;

    If X = 10 days, Y = 69.9%

    If X = 20 days, Y = 69.8%

    If X is 30 days, Y = 69.7%

    (B) The rate at which approval rating drops is very slow; compared to the increase in number of days in office. A 10 day increase in number of days in office only results in a 0.1 or 10% decrease in percentage approval ratings.

    (C) The longer a politician stays in office, the less his approval rating.

    (D) The percentage approval rating is greatly influenced or increased by the constant term 70
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